BAYESIAN ESTIMATION OF LATENT ROOTS AND VECTORS, WITH SPECIAL REFERENCE TO THE BIVARIATE NORMAL DISTRIBUTION.

摘要

The paper discusses some aspects of the estimation of latent roots and vectors of the covariance matrix of the bivariate normal distribution from a Bayesian viewpoint. The joint distribution of (1) the angle of the canonical transformation and (2) the ratio of the larger root to the total variance is considered in detail and illustrated by an example. Also discussed is the problem of making inferences about the larger roots,and several simple approximations to its distribution are considered. Finally a generalization of one of the approximation methods to latent roots of higher dimensional convariance matrix is given. (Author)